Abstract

We present an algorithm for generating a surface approximation of microcrystalline silicon (μc-Si) layers after plasma enhanced chemical vapor deposition (PECVD) onto surface textured substrates, where data of the textured substrate surface are available as input. We utilize mathematical image processing tools and combine them with an ellipsoid generator approach. The presented algorithm has been tuned for use in thin-film silicon solar cell applications, where textured surfaces are used to improve light trapping. We demonstrate the feasibility of this method by means of optical simulations of generated surface textures, comparing them to simulations of measured atomic force microscopy (AFM) scan data of both Aluminum-doped zinc oxide (AZO, a transparent and conductive material) and μc-Si layers.

© 2013 OSA

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  1. M. Ermes, K. Bittkau, R. Carius, “Influence of growth induced non-conformality on absorptance in silicon-based thin-film solar cells investigated by rigorous optical simulations,” Appl. Phys. Lett., to be submitted.
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    [CrossRef]
  4. V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
    [CrossRef]
  5. V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Opt. Express 21, A595–A606 (2013).
    [CrossRef]
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  7. V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013).
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  13. S. Yan, J. Krantz, K. Forberich, C. Pflaum, C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).
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    [CrossRef]
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  21. C. Jandl, K. Hertel, C. Pflaum, H. Stiebig, “Simulation of silicon thin-film solar cells for oblique incident waves,” in Eco-Photonics 2011: Sustainable Design, Manufacturing, and Engineering Workforce Education for a Green Future, P. Ambs, D. Curticapean, C. Emmelmann, W. Knapp, Z. T. Kuznicki, P. P. Meyrueis, eds., Proc. SPIE8065, pp. 806505 (2011).
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    [CrossRef]
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    [CrossRef]
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2013 (6)

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013).
[CrossRef] [PubMed]

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

S. Yan, J. Krantz, K. Forberich, C. Pflaum, C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
[CrossRef]

Y. Li, B. Qian, C. Li, J. Xu, C. Jiang, “Optical properties of nanocrystal-silicon thin films on silicon nanopillar arrays after thermal annealing,” Appl. Surf. Sci. 265, 324–328 (2013).
[CrossRef]

V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Opt. Express 21, A595–A606 (2013).
[CrossRef]

2011 (3)

J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett. 99(13), 131114–131114 (2011).
[CrossRef]

U. Pätzold, E. Moulin, B. Pieters, R. Carius, U. Rau, “Design of nanostructured plasmonic back contacts for thin-film silicon solar cells,” Opt. Express 19, A1219–A1230 (2011).
[CrossRef]

C. Pflaum, Z. Rahimi, “An iterative solver for the finite-difference frequency-domain (FDFD) method for the simulation of materials with negative permittivity,” Numer. Linear Algebra Appl. 18(4), 653–670 (2011).
[CrossRef]

2010 (3)

C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn, A. Gombert, eds., Proc. SPIE 7725, 772516 (2010).
[CrossRef]

H. Sai, H. Jia, M. Kondo, “Impact of front and rear texture of thin-film microcrystalline silicon solar cells on their light trapping properties,” Appl. Phys. 108(4), 044505 (2010).

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

2009 (1)

H. Sai, M. Kondo, “Effect of self-orderly textured back reflectors on light trapping in thin-film microcrystalline silicon solar cells,” Appl. Phys. 105(9), 094511 (2009).

2007 (2)

R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

P. I. Widenborg, A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass super-strates,” Adv. OptoElectron. 2007,24584-1–24584-7 (2007).
[CrossRef]

2004 (1)

J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

2001 (1)

S. J. Linz, M. Raible, P. Hänggi, “Amorphous thin film growth: modeling and pattern formation,” Adv. Solid State Phys. 41, 391–403 (2001).
[CrossRef]

2000 (1)

M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000).
[CrossRef]

1996 (1)

R. Malladi, J. A. Sethian, “Image processing: flows under min/max curvature and mean curvature,” Graph. Model. Image Process. 58(2), 127–141 (1996).
[CrossRef]

1990 (1)

P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[CrossRef]

1987 (1)

R. M. Haralick, S. R. Sternberg, X. Zhuang, “Image analysis using mathematical morphology,” IEEE Trans. Pattern Anal. Mach. Intell. 9(4), 532–550 (1987).
[CrossRef] [PubMed]

Aberle, A. G.

P. I. Widenborg, A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass super-strates,” Adv. OptoElectron. 2007,24584-1–24584-7 (2007).
[CrossRef]

Bhattacharya, J.

J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett. 99(13), 131114–131114 (2011).
[CrossRef]

Biswas, R.

J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett. 99(13), 131114–131114 (2011).
[CrossRef]

Bittkau, K.

M. Ermes, K. Bittkau, R. Carius, “Influence of growth induced non-conformality on absorptance in silicon-based thin-film solar cells investigated by rigorous optical simulations,” Appl. Phys. Lett., to be submitted.

Brabec, C.

S. Yan, J. Krantz, K. Forberich, C. Pflaum, C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).

Carius, R.

U. Pätzold, E. Moulin, B. Pieters, R. Carius, U. Rau, “Design of nanostructured plasmonic back contacts for thin-film silicon solar cells,” Opt. Express 19, A1219–A1230 (2011).
[CrossRef]

M. Ermes, K. Bittkau, R. Carius, “Influence of growth induced non-conformality on absorptance in silicon-based thin-film solar cells investigated by rigorous optical simulations,” Appl. Phys. Lett., to be submitted.

Chakravarty, N.

J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett. 99(13), 131114–131114 (2011).
[CrossRef]

Colding, T. H.

T. H. Colding, W. P. Minicozzi, “A Course in Minimal Surfaces” in Graduate Studies in Mathematics (American Mathematical Society, 2011), Vol. 121.

Cootes, T. F.

A. Lanitis, C. J. Taylor, T. F. Cootes, “Modeling the process of ageing in face images,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (Kerkyra, Greece, 1999) 1, pp. 131–136.

Dalal, V. L.

J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett. 99(13), 131114–131114 (2011).
[CrossRef]

Dewald, W.

C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn, A. Gombert, eds., Proc. SPIE 7725, 772516 (2010).
[CrossRef]

C. Jandl, W. Dewald, C. Pflaum, H. Stiebig, “Simulation of microcrystalline thin-film silicon solar cells with integrated AFM scans,” in Proceedings of the 25th European PV Solar Energy Conference and Exhibition (Valencia, Spain, 2010), pp. 3154–3157

Ermes, M.

M. Ermes, K. Bittkau, R. Carius, “Influence of growth induced non-conformality on absorptance in silicon-based thin-film solar cells investigated by rigorous optical simulations,” Appl. Phys. Lett., to be submitted.

Forberich, K.

S. Yan, J. Krantz, K. Forberich, C. Pflaum, C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).

Franken, R.

R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

Gall, S.

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

Gordijn, A.

C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn, A. Gombert, eds., Proc. SPIE 7725, 772516 (2010).
[CrossRef]

Hänggi, P.

S. J. Linz, M. Raible, P. Hänggi, “Amorphous thin film growth: modeling and pattern formation,” Adv. Solid State Phys. 41, 391–403 (2001).
[CrossRef]

M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000).
[CrossRef]

Haralick, R. M.

R. M. Haralick, S. R. Sternberg, X. Zhuang, “Image analysis using mathematical morphology,” IEEE Trans. Pattern Anal. Mach. Intell. 9(4), 532–550 (1987).
[CrossRef] [PubMed]

Hertel, K.

C. Jandl, K. Hertel, C. Pflaum, H. Stiebig, “Simulation of silicon thin-film solar cells for oblique incident waves,” in Eco-Photonics 2011: Sustainable Design, Manufacturing, and Engineering Workforce Education for a Green Future, P. Ambs, D. Curticapean, C. Emmelmann, W. Knapp, Z. T. Kuznicki, P. P. Meyrueis, eds., Proc. SPIE8065, pp. 806505 (2011).

Hrunski, D.

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

Hüpkes, J.

V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Opt. Express 21, A595–A606 (2013).
[CrossRef]

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
[CrossRef]

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013).
[CrossRef] [PubMed]

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

Jandl, C.

C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn, A. Gombert, eds., Proc. SPIE 7725, 772516 (2010).
[CrossRef]

C. Jandl, K. Hertel, C. Pflaum, H. Stiebig, “Simulation of silicon thin-film solar cells for oblique incident waves,” in Eco-Photonics 2011: Sustainable Design, Manufacturing, and Engineering Workforce Education for a Green Future, P. Ambs, D. Curticapean, C. Emmelmann, W. Knapp, Z. T. Kuznicki, P. P. Meyrueis, eds., Proc. SPIE8065, pp. 806505 (2011).

C. Jandl, W. Dewald, C. Pflaum, H. Stiebig, “Simulation of microcrystalline thin-film silicon solar cells with integrated AFM scans,” in Proceedings of the 25th European PV Solar Energy Conference and Exhibition (Valencia, Spain, 2010), pp. 3154–3157

Jia, H.

H. Sai, H. Jia, M. Kondo, “Impact of front and rear texture of thin-film microcrystalline silicon solar cells on their light trapping properties,” Appl. Phys. 108(4), 044505 (2010).

Jiang, C.

Y. Li, B. Qian, C. Li, J. Xu, C. Jiang, “Optical properties of nanocrystal-silicon thin films on silicon nanopillar arrays after thermal annealing,” Appl. Surf. Sci. 265, 324–328 (2013).
[CrossRef]

Jovanov, V.

V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Opt. Express 21, A595–A606 (2013).
[CrossRef]

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
[CrossRef]

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013).
[CrossRef] [PubMed]

Kluth, O.

J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

Knipp, D.

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013).
[CrossRef] [PubMed]

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
[CrossRef]

V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Opt. Express 21, A595–A606 (2013).
[CrossRef]

Konagai, M.

Kondo, M.

H. Sai, H. Jia, M. Kondo, “Impact of front and rear texture of thin-film microcrystalline silicon solar cells on their light trapping properties,” Appl. Phys. 108(4), 044505 (2010).

H. Sai, M. Kondo, “Effect of self-orderly textured back reflectors on light trapping in thin-film microcrystalline silicon solar cells,” Appl. Phys. 105(9), 094511 (2009).

Krantz, J.

S. Yan, J. Krantz, K. Forberich, C. Pflaum, C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).

Krc, J.

M. Sever, B. Lipovsek, J. Krc, M. Topic, “Optimisation of surface textures in thin-film silicon solar cells with 3d optical modelling by considering realistic layer growth,” in Proceedings of the 27th European PV Solar Energy Conference and Exhibition (Frankfurt, Germany, 2012), pp. 2129–2131.

Lanitis, A.

A. Lanitis, C. J. Taylor, T. F. Cootes, “Modeling the process of ageing in face images,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (Kerkyra, Greece, 1999) 1, pp. 131–136.

Lee, K.

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

Li, C.

Y. Li, B. Qian, C. Li, J. Xu, C. Jiang, “Optical properties of nanocrystal-silicon thin films on silicon nanopillar arrays after thermal annealing,” Appl. Surf. Sci. 265, 324–328 (2013).
[CrossRef]

Li, H.

R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

Li, Y.

Y. Li, B. Qian, C. Li, J. Xu, C. Jiang, “Optical properties of nanocrystal-silicon thin films on silicon nanopillar arrays after thermal annealing,” Appl. Surf. Sci. 265, 324–328 (2013).
[CrossRef]

Linz, S. J.

S. J. Linz, M. Raible, P. Hänggi, “Amorphous thin film growth: modeling and pattern formation,” Adv. Solid State Phys. 41, 391–403 (2001).
[CrossRef]

M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000).
[CrossRef]

Lipovsek, B.

M. Sever, B. Lipovsek, J. Krc, M. Topic, “Optimisation of surface textures in thin-film silicon solar cells with 3d optical modelling by considering realistic layer growth,” in Proceedings of the 27th European PV Solar Energy Conference and Exhibition (Frankfurt, Germany, 2012), pp. 2129–2131.

Magnus, P.

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Opt. Express 21, A595–A606 (2013).
[CrossRef]

Malik, J.

P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[CrossRef]

Malladi, R.

R. Malladi, J. A. Sethian, “Image processing: flows under min/max curvature and mean curvature,” Graph. Model. Image Process. 58(2), 127–141 (1996).
[CrossRef]

Mayr, S. G.

M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000).
[CrossRef]

Minicozzi, W. P.

T. H. Colding, W. P. Minicozzi, “A Course in Minimal Surfaces” in Graduate Studies in Mathematics (American Mathematical Society, 2011), Vol. 121.

Moske, M.

M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000).
[CrossRef]

Moulin, E.

Müller, J.

J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

Paetzold, U. W.

C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn, A. Gombert, eds., Proc. SPIE 7725, 772516 (2010).
[CrossRef]

Palanchoke, U.

Pattnaik, S.

J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett. 99(13), 131114–131114 (2011).
[CrossRef]

Pätzold, U.

Perona, P.

P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[CrossRef]

Pflaum, C.

S. Yan, J. Krantz, K. Forberich, C. Pflaum, C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).

C. Pflaum, Z. Rahimi, “An iterative solver for the finite-difference frequency-domain (FDFD) method for the simulation of materials with negative permittivity,” Numer. Linear Algebra Appl. 18(4), 653–670 (2011).
[CrossRef]

C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn, A. Gombert, eds., Proc. SPIE 7725, 772516 (2010).
[CrossRef]

C. Jandl, W. Dewald, C. Pflaum, H. Stiebig, “Simulation of microcrystalline thin-film silicon solar cells with integrated AFM scans,” in Proceedings of the 25th European PV Solar Energy Conference and Exhibition (Valencia, Spain, 2010), pp. 3154–3157

C. Jandl, K. Hertel, C. Pflaum, H. Stiebig, “Simulation of silicon thin-film solar cells for oblique incident waves,” in Eco-Photonics 2011: Sustainable Design, Manufacturing, and Engineering Workforce Education for a Green Future, P. Ambs, D. Curticapean, C. Emmelmann, W. Knapp, Z. T. Kuznicki, P. P. Meyrueis, eds., Proc. SPIE8065, pp. 806505 (2011).

Pieters, B.

Planchoke, U.

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

Poruba, A.

J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

Qian, B.

Y. Li, B. Qian, C. Li, J. Xu, C. Jiang, “Optical properties of nanocrystal-silicon thin films on silicon nanopillar arrays after thermal annealing,” Appl. Surf. Sci. 265, 324–328 (2013).
[CrossRef]

Rahimi, Z.

C. Pflaum, Z. Rahimi, “An iterative solver for the finite-difference frequency-domain (FDFD) method for the simulation of materials with negative permittivity,” Numer. Linear Algebra Appl. 18(4), 653–670 (2011).
[CrossRef]

Raible, M.

S. J. Linz, M. Raible, P. Hänggi, “Amorphous thin film growth: modeling and pattern formation,” Adv. Solid State Phys. 41, 391–403 (2001).
[CrossRef]

M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000).
[CrossRef]

Rath, J.

R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

Rau, U.

Rech, B.

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

Rockstuhl, C.

Roczen, M.

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

Ruske, F.

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

Sai, H.

H. Sai, H. Jia, M. Kondo, “Impact of front and rear texture of thin-film microcrystalline silicon solar cells on their light trapping properties,” Appl. Phys. 108(4), 044505 (2010).

H. Sai, M. Kondo, “Effect of self-orderly textured back reflectors on light trapping in thin-film microcrystalline silicon solar cells,” Appl. Phys. 105(9), 094511 (2009).

Samwer, K.

M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000).
[CrossRef]

Schropp, R.

R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

Schulte, M.

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013).
[CrossRef] [PubMed]

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
[CrossRef]

Sethian, J. A.

R. Malladi, J. A. Sethian, “Image processing: flows under min/max curvature and mean curvature,” Graph. Model. Image Process. 58(2), 127–141 (1996).
[CrossRef]

Sever, M.

M. Sever, B. Lipovsek, J. Krc, M. Topic, “Optimisation of surface textures in thin-film silicon solar cells with 3d optical modelling by considering realistic layer growth,” in Proceedings of the 27th European PV Solar Energy Conference and Exhibition (Frankfurt, Germany, 2012), pp. 2129–2131.

Shrestha, S.

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
[CrossRef]

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013).
[CrossRef] [PubMed]

Sichanugrist, P.

Slafer, W. D.

J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett. 99(13), 131114–131114 (2011).
[CrossRef]

Springer, J.

J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

Sternberg, S. R.

R. M. Haralick, S. R. Sternberg, X. Zhuang, “Image analysis using mathematical morphology,” IEEE Trans. Pattern Anal. Mach. Intell. 9(4), 532–550 (1987).
[CrossRef] [PubMed]

Stiebig, H.

V. Jovanov, U. Palanchoke, P. Magnus, H. Stiebig, J. Hüpkes, P. Sichanugrist, M. Konagai, S. Wiesendanger, C. Rockstuhl, D. Knipp, “Light trapping in periodically textured amorphous silicon thin film solar cells using realistic interface morphologies,” Opt. Express 21, A595–A606 (2013).
[CrossRef]

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn, A. Gombert, eds., Proc. SPIE 7725, 772516 (2010).
[CrossRef]

C. Jandl, W. Dewald, C. Pflaum, H. Stiebig, “Simulation of microcrystalline thin-film silicon solar cells with integrated AFM scans,” in Proceedings of the 25th European PV Solar Energy Conference and Exhibition (Valencia, Spain, 2010), pp. 3154–3157

C. Jandl, K. Hertel, C. Pflaum, H. Stiebig, “Simulation of silicon thin-film solar cells for oblique incident waves,” in Eco-Photonics 2011: Sustainable Design, Manufacturing, and Engineering Workforce Education for a Green Future, P. Ambs, D. Curticapean, C. Emmelmann, W. Knapp, Z. T. Kuznicki, P. P. Meyrueis, eds., Proc. SPIE8065, pp. 806505 (2011).

Stolk, R.

R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

Taylor, C. J.

A. Lanitis, C. J. Taylor, T. F. Cootes, “Modeling the process of ageing in face images,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (Kerkyra, Greece, 1999) 1, pp. 131–136.

Topic, M.

M. Sever, B. Lipovsek, J. Krc, M. Topic, “Optimisation of surface textures in thin-film silicon solar cells with 3d optical modelling by considering realistic layer growth,” in Proceedings of the 27th European PV Solar Energy Conference and Exhibition (Frankfurt, Germany, 2012), pp. 2129–2131.

van der Werf, C.

R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

Vanecek, M.

J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

Widenborg, P. I.

P. I. Widenborg, A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass super-strates,” Adv. OptoElectron. 2007,24584-1–24584-7 (2007).
[CrossRef]

Wiesendanger, S.

Wimmer, M.

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

Xu, J.

Y. Li, B. Qian, C. Li, J. Xu, C. Jiang, “Optical properties of nanocrystal-silicon thin films on silicon nanopillar arrays after thermal annealing,” Appl. Surf. Sci. 265, 324–328 (2013).
[CrossRef]

Xu, X.

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
[CrossRef]

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013).
[CrossRef] [PubMed]

X. Xu, “Nanotexturierte Grenzflächen in Silizium-Dünnschichtsolarzellen,” unpublished master’s thesis, Forschungszentrum Jülich, Germany (2011).

Yan, S.

S. Yan, J. Krantz, K. Forberich, C. Pflaum, C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).

Zeman, M.

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
[CrossRef]

Zhuang, X.

R. M. Haralick, S. R. Sternberg, X. Zhuang, “Image analysis using mathematical morphology,” IEEE Trans. Pattern Anal. Mach. Intell. 9(4), 532–550 (1987).
[CrossRef] [PubMed]

ACS Appl. Mater. Interfaces (1)

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, D. Knipp, “Predicting the interface morphologies of silicon films on arbitrary substrates: application in solar cells,” ACS Appl. Mater. Interfaces 5(15), 7109–7116 (2013).
[CrossRef] [PubMed]

Adv. OptoElectron. (1)

P. I. Widenborg, A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass super-strates,” Adv. OptoElectron. 2007,24584-1–24584-7 (2007).
[CrossRef]

Adv. Solid State Phys. (1)

S. J. Linz, M. Raible, P. Hänggi, “Amorphous thin film growth: modeling and pattern formation,” Adv. Solid State Phys. 41, 391–403 (2001).
[CrossRef]

Appl. Phys. (6)

H. Sai, M. Kondo, “Effect of self-orderly textured back reflectors on light trapping in thin-film microcrystalline silicon solar cells,” Appl. Phys. 105(9), 094511 (2009).

F. Ruske, M. Roczen, K. Lee, M. Wimmer, S. Gall, J. Hüpkes, D. Hrunski, B. Rech, “Improved electrical transport in Al-doped zinc oxide by thermal treatment,” Appl. Phys. 107(1), 013708 (2010).

J. Springer, A. Poruba, J. Müller, M. Vanecek, O. Kluth, B. Rech, “Absorption loss at nanorough silver back reflector of thin-film silicon solar cells,” Appl. Phys. 95(3), 1427–1429 (2004).

R. Franken, R. Stolk, H. Li, C. van der Werf, J. Rath, R. Schropp, “Understanding light trapping by light scattering textured back electrodes in thin film n-i-p-type silicon solar cells,” Appl. Phys. 102(1), 014503 (2007).

S. Yan, J. Krantz, K. Forberich, C. Pflaum, C. Brabec, “Numerical simulation of light propagation in silver nanowire films using time-harmonic inverse iteration method,” Appl. Phys. 113(15), 154303 (2013).

H. Sai, H. Jia, M. Kondo, “Impact of front and rear texture of thin-film microcrystalline silicon solar cells on their light trapping properties,” Appl. Phys. 108(4), 044505 (2010).

Appl. Phys. Lett. (1)

J. Bhattacharya, N. Chakravarty, S. Pattnaik, W. D. Slafer, R. Biswas, V. L. Dalal, “A photonic-plasmonic structure for enhancing light absorption in thin film solar cells,” Appl. Phys. Lett. 99(13), 131114–131114 (2011).
[CrossRef]

Appl. Surf. Sci. (1)

Y. Li, B. Qian, C. Li, J. Xu, C. Jiang, “Optical properties of nanocrystal-silicon thin films on silicon nanopillar arrays after thermal annealing,” Appl. Surf. Sci. 265, 324–328 (2013).
[CrossRef]

Europhys. Lett. (1)

M. Raible, S. G. Mayr, S. J. Linz, M. Moske, P. Hänggi, K. Samwer, “Amorphous thin-film growth: theory compared with experiment,” Europhys. Lett. 50(1), 61–67 (2000).
[CrossRef]

Graph. Model. Image Process. (1)

R. Malladi, J. A. Sethian, “Image processing: flows under min/max curvature and mean curvature,” Graph. Model. Image Process. 58(2), 127–141 (1996).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (2)

R. M. Haralick, S. R. Sternberg, X. Zhuang, “Image analysis using mathematical morphology,” IEEE Trans. Pattern Anal. Mach. Intell. 9(4), 532–550 (1987).
[CrossRef] [PubMed]

P. Perona, J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990).
[CrossRef]

Numer. Linear Algebra Appl. (1)

C. Pflaum, Z. Rahimi, “An iterative solver for the finite-difference frequency-domain (FDFD) method for the simulation of materials with negative permittivity,” Numer. Linear Algebra Appl. 18(4), 653–670 (2011).
[CrossRef]

Opt. Express (2)

Photonics for Solar Energy Systems III Proc. SPIE (1)

C. Jandl, W. Dewald, U. W. Paetzold, A. Gordijn, C. Pflaum, H. Stiebig, “Simulation of tandem thin-film silicon solar cells,” in Photonics for Solar Energy Systems III, R. B. Wehrspohn, A. Gombert, eds., Proc. SPIE 7725, 772516 (2010).
[CrossRef]

Sol. Energy Mater. Sol. Cells (2)

V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013).
[CrossRef]

V. Jovanov, X. Xu, S. Shrestha, M. Schulte, J. Hüpkes, M. Zeman, D. Knipp, “Influence of interface morphologies on amorphous silicon thin film solar cells prepared on randomly textured substrates,” Sol. Energy Mater. Sol. Cells 112, 182–189 (2013).
[CrossRef]

Other (8)

M. Sever, B. Lipovsek, J. Krc, M. Topic, “Optimisation of surface textures in thin-film silicon solar cells with 3d optical modelling by considering realistic layer growth,” in Proceedings of the 27th European PV Solar Energy Conference and Exhibition (Frankfurt, Germany, 2012), pp. 2129–2131.

A. Lanitis, C. J. Taylor, T. F. Cootes, “Modeling the process of ageing in face images,” in Proceedings of the Seventh IEEE International Conference on Computer Vision (Kerkyra, Greece, 1999) 1, pp. 131–136.

C. Jandl, W. Dewald, C. Pflaum, H. Stiebig, “Simulation of microcrystalline thin-film silicon solar cells with integrated AFM scans,” in Proceedings of the 25th European PV Solar Energy Conference and Exhibition (Valencia, Spain, 2010), pp. 3154–3157

C. Jandl, K. Hertel, C. Pflaum, H. Stiebig, “Simulation of silicon thin-film solar cells for oblique incident waves,” in Eco-Photonics 2011: Sustainable Design, Manufacturing, and Engineering Workforce Education for a Green Future, P. Ambs, D. Curticapean, C. Emmelmann, W. Knapp, Z. T. Kuznicki, P. P. Meyrueis, eds., Proc. SPIE8065, pp. 806505 (2011).

X. Xu, “Nanotexturierte Grenzflächen in Silizium-Dünnschichtsolarzellen,” unpublished master’s thesis, Forschungszentrum Jülich, Germany (2011).

T. H. Colding, W. P. Minicozzi, “A Course in Minimal Surfaces” in Graduate Studies in Mathematics (American Mathematical Society, 2011), Vol. 121.

M. Mondelli, A. Ciomaga, “Finite difference schemes for MCM and AMSS,” Image processing on line 2011, http://dx.doi.org/10.5201/ipol.2011.cm_fds .

M. Ermes, K. Bittkau, R. Carius, “Influence of growth induced non-conformality on absorptance in silicon-based thin-film solar cells investigated by rigorous optical simulations,” Appl. Phys. Lett., to be submitted.

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